Illustrating field emission theory by using Lauritsen plots of transmission probability and barrier strength

TL;DR

This paper introduces Lauritsen plots of transmission probability and barrier strength as visual tools to better understand cold field electron emission theory, supplementing traditional Fowler-Nordheim plots.

Contribution

It proposes using Lauritsen plots for barrier strength and transmission probability to illustrate key aspects of tunnelling theory in CFE, including analytical approximations for Coulomb barriers.

Findings

Lauritsen plots effectively illustrate tunnelling barrier effects.

Analytical series approximation for Coulomb barrier correction factor.

Curvature in FN plots can be predicted using these methods.

Abstract

This technical note relates to the theory of cold field electron emission (CFE). It starts by suggesting that, to emphasize common properties in relation to CFE theory, the term 'Lauritsen plot' could be used to describe all graphical plots made with the reciprocal of barrier field (or the reciprocal of a quantity proportional to barrier field) on the horizontal axis. It then argues that Lauritsen plots related to barrier strength (G) and transmission probability (D) could play a useful role in discussion of CFE theory. Such plots would supplement conventional Fowler-Nordheim (FN) plots. All these plots would be regarded as particular types of Lauritsen plot. The Lauritsen plots of -G and lnD can be used to illustrate how basic aspects of FN tunnelling theory are influenced by the mathematical form of the tunnelling barrier. These, in turn, influence local emission current density and emission current. Illustrative applications used in this note relate to the well-known exact triangular and Schottky-Nordheim barriers, and to the Coulomb barrier (i.e., the electrostatic component of the electron potential energy barrier outside a model spherical emitter). For the Coulomb barrier, a good analytical series approximation has been found for the barrier-form correction factor; this can be used to predict the existence (and to some extent the properties) of related curvature in FN plots.